Ceramic matrix composites, which include ceramic fibers embedded in a ceramic matrix, exhibit a combination of properties that make them promising candidates for industrial applications that demand excellent thermal and mechanical properties along with low weight, such as gas turbine engine components. Existing CMCs and turbine engine components systems have various shortcomings, however, such as the ability to function at high temperatures without sacrificing structural stability. As CMC parts see increasing use as replacements for current metallic flowpath components in turbine engines, CMC-compatible cooling techniques are becoming increasingly important. Various cooling schemes have been attempted for CMC components, such as the placement of a series of continuous tubes into the fibrous preform of the composite during fabrication. It would be advantageous to develop a CMC component with integral cooling capabilities that can maintain a more uniform operating temperature, particularly for complex geometric parts.